Temporal scaling comparison of real hydrological data and model runoff records (original) (raw)
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Long-term persistence and multifractality of river runoff records: Detrended fluctuation studies
Journal of Hydrology, 2006
We study temporal correlations and multifractal properties of long river discharge records from 41 hydrological stations around the globe. To detect long-term correlations and multifractal behaviour in the presence of trends, we apply several recently developed methods [detrended fluctuation analysis (DFA), wavelet analysis, and multifractal DFA] that can systematically detect and overcome nonstationarities in the data at all time scales. We find that above some crossover time that usually is several weeks, the daily runoffs are long-term correlated, being characterized by a correlation function C(s) that decays as C(s) ∼ s −γ . The exponent γ varies from river to river in a wide range between 0.1 and 0.9. The power-law decay of C(s) corresponds to a power-law increase of the related fluctuation function F 2 (s) ∼ s H where H = 1 − γ/2. We also find that in most records, for large times, weak multifractality occurs. The Renyi exponent τ (q) for q between −10 and +10 can be fitted to the remarkably simple form τ (q) = − ln(a q + b q )/ ln 2, with solely two parameters a and b between 0 and 1 with a + b ≥ 1. This type of multifractality is obtained from a generalization of the multiplicative cascade model.
Long-term persistence and multifractality of precipitation and river runoff records
Journal of Geophysical Research, 2006
1] We discuss and compare the multifractal temporal scaling properties of precipitation and river discharge records on large timescales. To detect long-term correlations and multifractal behavior in the presence of trends, we apply recently developed methods (detrended fluctuation analysis (DFA) and multifractal DFA) that can systematically detect nonstationarities and overcome trends in the data at all timescales. We find that above some crossover time that usually is several weeks, the daily runoffs are characterized by an asymptotic scaling exponent that indicates a slow power law decay of the runoff autocorrelation function and varies from river to river in a wide range. Below the crossovers, pronounced short-term correlations occur. In contrast, most of the precipitation series show scaling behavior corresponding to a rapid decay of the autocorrelation function. For the multifractal characterization of the data we determine the generalized Hurst exponents and fit them by three operational models. While the fits based on the universal multifractal model describe well the scaling behavior of the positive moments in nearly all runoff and precipitation records, positive as well as negative moments are consistent with two-parameter fits from a modified version of the multiplicative cascade model for all runoff records and most of the precipitation records. For some precipitation records with weak multifractality, however, a simple bifractal characterization gives the best fit of the data.
Physica A: Statistical Mechanics and its Applications, 2003
We study the multifractal temporal scaling properties of river discharge and precipitation records. We compare the results for the multifractal detrended fluctuation analysis method with the results for the wavelet transform modulus maxima technique and obtain agreement within the error margins. In contrast to previous studies, we find non-universal behaviour: On long time scales, above a crossover time scale of several months, the runoff records are described by fluctuation exponents varying from river to river in a wide range. Similar variations are observed for the precipitation records which exhibit weaker, but still significant multifractality. For all runoff records the type of multifractality is consistent with a modified version of the binomial multifractal model, while several precipitation records seem to require different models.
Stochastic Environmental Research and Risk Assessment, 2009
We analyzed long daily runoff series at six hydrological stations located along the mainstem Yellow River basin by using power spectra analysis and multifractal detrended fluctuation analysis (MF-DFA) technique with aim to deeply understand the scaling properties of the hydrological series in the Yellow River basin. Research results indicate that: (1) the runoff fluctuations of the Yellow River basin exhibit self-affine fractal behavior and different memory properties at different time scales. Different crossover frequency (1/f) indicates that lower crossover frequency usually corresponds to larger basin area, and vice versa, showing the influences of river size on higher frequency of runoff variations. This may be due to considerable regulations of river channel on the runoff variations in river basin of larger basin size; (2) the runoff fluctuations in the Yellow River basin exhibit short-term memory properties at smaller time scales. Crossover analysis by MF-DFA indicates unchanged annual cycle within the runoff variations, implying dominant influences of climatic changes on changes of runoff amount at longer time scales, e.g. 1 year. Human activities, such as human withdrawal of freshwater and construction of water reservoirs, in different reaches of the Yellow River basin may be responsible for different scaling properties of runoff variations in the Yellow River basin. The results of this study will be helpful for hydrological modeling in different time scales and also for water resource management in the arid and semi-arid regions of China.
In order to determine objectively the fractal behaviour of a time series, and to facilitate potential future attempts to assess model performance by incorporating fractal behaviour, a multi-order robust detrended fluctuation analysis (r-DFAn) procedure is developed herein. The r-DFAn procedure allows for robust and automated quantification of mono-fractal behaviour. The fractal behaviour is quantified with three parts: a global scaling exponent, crossovers, and local scaling exponents. The robustness of the r-DFAn procedure is established by the systematic use of robust regression, piecewise linear regression , Analysis of Covariance (ANCOVA) and Multiple Comparison Procedure to determine statistically significant scaling exponents and optimum crossover locations. The MATLAB code implementing the r-DFAn procedure has also been open sourced to enable reproducible results. r-DFAn will be illustrated on a synthetic signal after which is used to analyse high-resolution hydro-logic data; although the r-DFAn procedure is not limited to hydrological or geophysical time series. The hydrological data are 4 year-long datasets (January 2012 to January 2016) of 1-min groundwater level, river stage, groundwater and river temperature, and 15-min precipitation and air temperature, at Wallingford, UK. The datasets are analysed in both time and fractal domains. The study area is a shallow riparian aquifer in hydraulic connection to River Thames, which traverses the site. The unusually high resolution datasets, along with the responsive nature of the aquifer, enable detailed examination of the various data and their interconnections in both time-and fractal-domains.
SN Applied Sciences, 2018
This paper presents arbitrary-order Hilbert spectral analysis (AOHSA) and multifractal detrended fluctuation analysis (MF-DFA) approaches to describe the multifractality of daily streamflows from four stations, namely Tilga, Jeraikela, Gomlai and Jenapur of Brahmani river basin in India. In the former method, the spectral slopes of Hilbert spectra for different moment orders depict the multifractality, and in this study, AOHSA method detected the scale invariance between synoptic to intra-seasonal scales (3 days-3 months approximately) in the daily streamflows of all the four stations. The MF-DFA method detected a crossover within 80-110 days (~ 3 months) in the four time series in addition to the crossover at annual scale. The robust estimates of Hurst exponents made by following the adaptive detrending method of preprocessing detrending operation ranged between 0.7 and 0.73 for the four time series which confirmed the universal multifractal properties within Brahmani river basin. The behaviour of spectral slope plot of AOHSA, the characteristics of scaling exponent plot, mass exponent plot and multifractal spectra confirmed that the highest multifractal degree is for the streamflow records of Tilga station which is having the smallest drainage area, and it may be attributed to the faster response of this sub-catchment to local precipitation events. The multifractality of all the four streamflow time series is found to be due to the dominant influence of correlation properties than due to the broadness of probability density function.
Multifractal analysis of streamflow records of the East River basin (Pearl River), China
Physica A: Statistical Mechanics and its Applications, 2009
River flow Multifractal behavior Multifractal detrended fluctuation analysis (MF-DFA) East River basin Pearl River basin a b s t r a c t Scaling behaviors of the long daily streamflow series of four hydrological stamainstream East River, one of the tributaries of the Pearl River (Zhujiang River) basin, were analyzed using multifractal detrended fluctuation analysis (MF-DFA). The research results indicated that streamflow series of the East River basin are characterized by anti-persistence. MF-DFA technique showed similar scaling properties in the streamflow series of the East River basin on shorter time scales, indicating universal scaling properties over the East River basin. Different intercept values of the fitted lines of log-log curve of F q (s) versus s implied hydrological regulation of water reservoirs.
Journal of Hydrology, 1998
Multifractal analysis of the daily river flow data from 19 river basins of watershed areas ranging from 5 to 1.8 × 106 km 2 from the continental USA was performed. This showed that the daily river flow series were multifractal over a range of scales spanning at least 23 to 216 days. Although no outer limit to the scaling was found (and for one series this was as long as 74 years duration) for most of the rivers, there is a break in the scaling regime at a period of about one week which is comparable to the atmosphere's synoptic maximum, the typical lifetime of planetary-scale atmospheric structures. For scales longer than 8 days, the universal multifractal parameters characterizing the infinite hierarchy of scaling exponents were estimated. The parameter values were found to be close to those of (small basin) French rivers studied by . The multifractal parameters showed no systematic basin-to-basin variability; our results are compatible with random variations. The three basic universal multifractal parameters are not only robust over wide ranges of time scales, but also over wide ranges in basin size, presumably reflecting the space-time multiscaling of both the rainfall and runoff processes.
Fractal analysis of river flow fluctuations
Physica A-statistical Mechanics and Its Applications, 2008
We use some fractal analysis methods to study river flow fluctuations. The result of the Multifractal Detrended Fluctuation Analysis (MF-DFA) shows that there are two crossover timescales at s1× ∼ 12 and s2× ∼ 130 months in the fluctuation function. We discuss how the existence of the crossover timescales are related to a sinusoidal trend. The first crossover is due to the seasonal trend and the value of second ones is approximately equal to the well known cycle of sun activity. Using Fourier detrended fluctuation analysis, the sinusoidal trend is eliminated. The value of Hurst exponent of the runoff water of rivers without the sinusoidal trend shows a long range correlation behavior. For the Daugava river the value of Hurst exponent is 0.52 ± 0.01 and also we find that these fluctuations have multifractal nature. Comparing the MF-DFA results for the remaining data set of Daugava river to those for shuffled and surrogate series, we conclude that its multifractal nature is almost entirely due to the broadness of probability density function.